Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x-5y &= -5 \\ -8x+6y &= 2\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-8x = -6y+2$ Divide both sides by $-8$ to isolate $x$ $x = {\dfrac{3}{4}y - \dfrac{1}{4}}$ Substitute this expression for $x$ in the first equation. $3({\dfrac{3}{4}y - \dfrac{1}{4}}) - 5y = -5$ $\dfrac{9}{4}y - \dfrac{3}{4} - 5y = -5$ Simplify by combining terms, then solve for $y$ $-\dfrac{11}{4}y - \dfrac{3}{4} = -5$ $-\dfrac{11}{4}y = -\dfrac{17}{4}$ $y = \dfrac{17}{11}$ Substitute $\dfrac{17}{11}$ for $y$ in the top equation. $3x-5( \dfrac{17}{11}) = -5$ $3x-\dfrac{85}{11} = -5$ $3x = \dfrac{30}{11}$ $x = \dfrac{10}{11}$ The solution is $\enspace x = \dfrac{10}{11}, \enspace y = \dfrac{17}{11}$.